Proper curvature symmetry in non-static cylindrically symmetric Lorentzian manifolds

We considered the most general form of non-static cylindrically symmetric space-times for studying proper curvature symmetry by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature symmetry in each case of the above space-times it is shown that when the above space-times admit proper curvature symmetry, they form an infinite dimensional vector space.